Non-conservative Forces Research Articles

Ab Initio molecular dynamics with screened Lorentz forces. II. Efficient propagators and rovibrational spectra in strong magnetic fields.

Strong magnetic fields have a large impact on the dynamics of molecules. In addition to the changes in the electronic structure, the nuclei are exposed to the Lorentz force with the magnetic field being screened by the electrons. In this work, we explore these effects using ab initio molecular dynamics simulations based on an effective Hamiltonian calculated at the Hartree-Fock level of theory. To correctly include these non-conservative forces in the dynamics, we have designed a series of novel propagators that show both good efficiency and stability in test cases. As a first application, we analyze simulations of He and H2 at two field strengths characteristic of magnetic white dwarfs (0.1 B0 = 2.35 × 104 T and B0 = 2.35 × 105 T). While the He simulations clearly demonstrate the importance of electron screening of the Lorentz force in the dynamics, the extracted rovibrational spectra of H2 reveal a number of fascinating features not observed in the field-free case: couplings of rotations/vibrations with the cyclotron rotation, overtones with unusual selection rules, and hindered rotations that transmute into librations with increasing field strength. We conclude that our presented framework is a powerful tool to investigate molecules in these extreme environments.

On the modified least action principle with dissipation

The principle of least action is a variational principle that states an object will always take the path of least action as compared to any other conceivable path. This principle can be used to derive the equations of motion of many systems, and therefore provides a unifying equation that has been applied in many fields of physics and mathematics. Hamilton’s formulation of the principle of least action typically only accounts for conservative forces, but can be reformulated to include non-conservative forces such as friction by using the approach suggested by Wang and co-workers (Lin and Wang, 2014; Wang, 2015). However, it turns out that this modified action is dependent upon the nature and amount of damping in the system and the optimality argument fails to hold for sufficiently large values of the damping coefficient. In this paper, we specifically investigate the modified action principle for the cases of a linearly and cubically damped, nonlinear pendulum.

Students’ Difficulties in Applying the Law of Conservation of Mechanical Energy: Results of a Survey Research

The purpose of this study was to explore the effectiveness of the conventional high school instruction about conservation of mechanical energy in Canton Sarajevo. To that end we tested 441 high school students from six different schools in Sarajevo (Bosnia and Herzegovina) for their competence to apply the law of conservation of mechanical energy. Concretely, students were expected to solve 5 open-ended tasks that covered conceptually different situations. In each task we asked a set of sub-questions to check whether the students possess all the prerequisite sub-competencies for systematic reasoning about conservation of mechanical energy. In addition, we investigated how students’ ideas about conservation of mechanical energy were affected by the choice of the physical system, as well as by the choice of the observed time interval. Data analysis was performed on the level of individual tasks. The students’ written answers were analyzed and the frequencies of most prominent student responses were reported. Generally, it has been shown that most high school students from Sarajevo fail to identify and distinguish internal, external, conservative and non-conservative forces. Also, many students think that applicability of the conservation law does not depend on the chosen physical system and its evolution over time. We could conclude that high school students’ use of the conservation law is mostly based on remembering similar problem solving experiences, rather than on relevant strategic knowledge.

β-decay and isospin symmetry breaking

<p indent=0mm>The elegant concept of isospin symmetry is of fundamental importance in nuclear and elementary particle physics. As a β-decay process changes an up quark to a down quark or <italic>vice versa</italic>, studies of nuclei with exchanged numbers of neutrons and protons, known as mirror nuclei, can be a powerful means to probe isospin symmetry breaking. A series of β-decay experiments of sd-shell nuclei near the proton drip line produced by projectile fragmentation were performed at the Radioactive Ion Beam Line of the Heavy Ion Research Facility in Lanzhou (HIRFL-RIBLL1) using a silicon array with a high detection efficiency and a low detection threshold. The secondary ions were identified by the combination of Δ<italic>E</italic>-TOF and magnetic rigidity (<italic>Bρ</italic>) in which the time of flight (TOF) was measured by two plastic scintillators at the second and fourth focal planes of the RIBLL1 and the energy loss (Δ<italic>E</italic>) was measured by two silicon detectors in the front of the silicon array. Double-sided silicon strip detectors (DSSDs) in the center of the array served to measure the residual energies of secondary ions on an event-by-event basis and study their decay properties with an implantation-decay correlation. Several quadrant silicon detectors (QSDs) placed behind DSSDs were used for anticoincidences of the penetrating fragments and light particles coming along with the beam, and measurements of β particles and high-energy protons. The β-delayed proton peaks with known energies and their corresponding absolute intensities were used for the energy and detection efficiency calibrations of the DSSDs. The system allows us to measure protons with energies down to about <sc>200 keV</sc> without obvious β background in the proton spectrum and was successful to measure the energies, time, and positions of implanted ions and decay protons efficiently, supporting researchers to study the decay properties of nuclei towards the proton drip line. The β-decay data, together with the large-scale shell-model calculations, allows detailed investigations on the mirror-nuclei systems resulting in the systematic study of isospin symmetry breaking in the sd-shell nuclear region. It was found that the mirror asymmetry parameters become larger due to the smaller separation energies while approaching the proton drip line for the extremely proton-rich sulfur nuclei ^27,28,29S and the Coulomb forces and other isospin-symmetry nonconserving forces acting between protons would lead to extended proton wave functions and cause mirror asymmetries. The properties of ²²Si β-decay for the transitions to the low-lying states of ²²Al were measured, and the reduced transition probabilities were determined. Comparing with the data on the β-decay of the mirror nucleus ²²O, we found a mirror asymmetry of <italic>δ</italic>=209(96)% in the transition to the first 1⁺ excited state of the respective daughters. This is by far the largest value of <italic>δ</italic> observed in the low-lying states. Shell-model calculations with isospin-nonconserving forces, including the <italic>T</italic>=1,<italic> J</italic>=2, 3 interactions related to the s_1/2 orbit that introduces explicitly the isospin-symmetry breaking force and describes the loosely bound nature of the wave functions of the s_1/2 orbit, can reproduce the observed data well and demonstrate that this dramatically large mirror asymmetry is attributed to the significant proton occupation and loosely bound nature of the wave functions of the s_1/2 orbit, which suggests that ²²Al is a proton-halo nucleus.

Energy loss and jerk on the loop-the-loop

In its usual form, the loop-the-loop (LtL) problem involves a uniform solid sphere rolling from rest down a linear ramp that transitions into a circular loop. The task is to find the minimum height from which the ball must be released in order to roll completely around the loop without breaking contact. The answer, found using the conservation of mechanical energy and Newton's second law, is invariably less than the actual measured height. The difference, attributed to non-conservative forces, is consistently larger than the experimental uncertainty. To get a more detailed understanding of the effects of dissipative forces on the loop-the-loop, we made high speed video recordings of balls moving on the commercial LtL apparatus and used video analysis to study their motion in detail. We present our results along with a simple model to predict the motion of the ball on an LtL track taking energy losses into account. Calculations based on the model are in excellent agreement with our measurements.

An analysis of a priori and empirical solar radiation pressure models for GPS satellites

Abstract. Among the different non-conservative forces acting on GPS satellites, solar radiation pressure (SRP) has the greatest influence and inappropriate modeling of it can introduce an acceleration with the order of 1 × 10−7 m s−2. There are a variety of empirical, analytical, and hybrid empirical-physical models to describe the SRP effect. Among them, the empirical model developed at the Center for Orbit Determination in Europe (CODE) and analytical models based on a box-wing prototype, namely box-shape bus with solar panels, are widely used in the International GNSS Service (IGS) community. To investigate the effects of different a priori SRP models on top of empirical parameterization, two sets of parameters based on the Empirical CODE Orbit Model (ECOM) and two a priori models including the analytical box-wing model and the empirical GPS Solar Pressure Model (GSPM) are tested for the different GPS satellites. Orbit comparison of different SRP scenarios shows that: (1) the two parameterizations of ECOM perform differently for Block IIA and IIR/IIR-M satellites but lead to fewer differences for Block IIF satellites in terms of orbit difference pattern. The 3D RMS of orbit difference of two parameterizations are 25, 30 and 21 mm for each block type. (2) Adoption of a priori model or change of the ECOM parameterization mainly lead to orbit differences varying with both elevation of the Sun w.r.t. the orbit plane and the satellites' argument of latitude w.r.t. the noon point, which is supposed to be related to the special geometry and attitude of every block type. These differences are especially obvious in radial direction. Analysis of estimated parameters of ECOM indicates that (3) the GSPM.04 performs better than box-wing model to describe the main constant solar radiation. It is found (4) that the asymmetry of estimated ECOM parameters in B direction (i.e., the direction completing the orthogonal system with D direction and satellite's solar panel axes), observed for three Block IIR satellites, causes corresponding asymmetrical orbit differences in radial direction when reduced ECOM parameters are used. This does not apply to the extended ECOM parameterization tested in this study, which indicates the insufficiency of reduced ECOM to parameterize asymmetrical satellites.

Finding the strongest stable massless column with a follower load and relocatable concentrated masses

Summary We consider the problem of optimal placement of concentrated masses along a massless elastic column that is clamped at one end and loaded by a nonconservative follower force at the free end. The goal is to find the largest possible interval such that the variation in the loading parameter within this interval preserves stability of the structure. The stability constraint is nonconvex and nonsmooth, making the optimization problem quite challenging. We give a detailed analytical treatment for the case of two masses, arguing that the optimal parameter configuration approaches the flutter and divergence boundaries of the stability region simultaneously. Furthermore, we conjecture that this property holds for any number of masses, which in turn suggests a simple formula for the maximal load interval for $n$ masses. This conjecture is strongly supported by extensive computational results, obtained using the recently developed open-source software package granso (GRadient-based Algorithm for Non-Smooth Optimization) to maximize the load interval subject to an appropriate formulation of the nonsmooth stability constraint. We hope that our work will provide a foundation for new approaches to classical long-standing problems of stability optimization for nonconservative elastic systems arising in civil and mechanical engineering.

Data-driven reaction coordinate discovery in overdamped and non-conservative systems: application to optical matter structural isomerization

Optical matter (OM) systems consist of (nano-)particle constituents in solution that can self-organize into ordered arrays that are bound by electrodynamic interactions. They also manifest non-conservative forces, and the motions of the nano-particles are overdamped; i.e., they exhibit diffusive trajectories. We propose a data-driven approach based on principal components analysis (PCA) to determine the collective modes of non-conservative overdamped systems, such as OM structures, and harmonic linear discriminant analysis (HLDA) of time trajectories to estimate the reaction coordinate for structural transitions. We demonstrate the approach via electrodynamics-Langevin dynamics simulations of six electrodynamically-bound nanoparticles in an incident laser beam. The reaction coordinate we discover is in excellent accord with a rigorous committor analysis, and the identified mechanism for structural isomerization is in very good agreement with the experimental observations. The PCA-HLDA approach to data-driven discovery of reaction coordinates can aid in understanding and eventually controlling non-conservative and overdamped systems including optical and active matter systems.

Effects of Wave–Current Interaction on the Eastern China Coastal Waters during Super Typhoon Lekima (2019)

AbstractLekima was a devastating super typhoon hitting China in 2019. Here, we use a high-resolution wave–current coupling model to investigate the impacts of wave–current interaction during Lekima on wave height, storm surge, ocean currents, and momentum balance. The model results were in good agreement with observations. It was found that, in the open waters, the strong currents generated by the typhoon winds reduced the typhoon-induced maximum significant wave heights (MSWHs) by 6%–15%. The baroclinicity of seawater also slightly reduced the MSWHs by approximately 3%. In the coastal waters, the MSWHs were increased by 6%–15% when feedbacks from water levels were considered. The typhoon-induced highest storm surge occurred in the coastal waters right of the typhoon’s landing position. The nonconservative wave forces contributed by approximately 0.1–0.4 m to the most severe storm surge (3 m), with this effect being most prominent in coastal waters. The baroclinicity of seawater generally increased the storm surge but had little influence on very shallow waters. Tides tend to exacerbate storm surge in most nearshore waters, except in a small bay. Waves generally increased the velocity of offshore ocean currents via the wave-breaking-induced acceleration. A cross-shore momentum balance analysis shows that when the typhoon was near the shore, the dominant terms in the momentum equation were the horizontal pressure gradient force and the surface wind stress, and the contribution of wave breaking had similar pattern to that of the wind stress but a lower magnitude. Our findings have significant implications for the numerical modeling of typhoons and the prediction of their impacts in the coastal environment.

Escape dynamics of active particles in multistable potentials

Rare transitions between long-lived metastable states underlie a great variety of physical, chemical and biological processes. Our quantitative understanding of reactive mechanisms has been driven forward by the insights of transition state theory and in particular by Kramers’ dynamical framework. Its predictions, however, do not apply to systems that feature non-conservative forces or correlated noise histories. An important class of such systems are active particles, prominent in both biology and nanotechnology. Here, we study the active escape dynamics of a silica nanoparticle trapped in a bistable potential. We introduce activity by applying an engineered stochastic force that emulates self-propulsion. Our experiments, supported by a theoretical analysis, reveal the existence of an optimal correlation time that maximises the transition rate. We discuss the origins of this active turnover, reminiscent of the much celebrated Kramers turnover. Our work establishes a versatile experimental platform to study single particle dynamics in non-equilibrium settings.

Local detailed balance across scales: From diffusions to jump processes and beyond.

Diffusive dynamics in presence of deep energy minima and weak nongradient forces can be coarse grained into a mesoscopic jump process over the various basins of attraction. Combining standard weak-noise results with a path integral expansion around equilibrium, we show that the emerging transition rates satisfy local detailed balance (LDB). Namely, the log ratio of the transition rates between nearby basins of attractions equals the free-energy variation appearing at equilibrium, supplemented by the work done by the nonconservative forces along the typical transition path. When the mesoscopic dynamics possesses a large-size deterministic limit, it can be further reduced to a jump process over macroscopic states satisfying LDB. The persistence of LDB under coarse graining of weakly nonequilibrium states is a generic consequence of the fact that only dissipative effects matter close to equilibrium.

TEACHING UPPER-SECONDARY STUDENTS ABOUT CONSERVATION OF MECHANICAL ENERGY: TWO VARIANTS OF THE SYSTEM APPROACH TO ENERGY ANALYSIS

Conventional teaching about the law of conservation of mechanical energy (LCME) often results with students trying to solve problems by remembering similar problems they already covered in classes. Consequently, many students fail to transfer their knowledge to simplest real-life problems. Therefore, a pre-test – post-test quasi-experiment was conducted to evaluate the effects of an alternative, system-based approach to teaching about LCME. The study included 70 upper-secondary students from the First Bosniak Gymnasium Sarajevo, Bosnia and Herzegovina. Firstly, all students learned about energy in a conventional way. Then they wrote a test on LCME and had three additional hours of teaching about this topic, where one group of students learned in line with the forces-variant of the system approach (e.g., discussing conservative and non-conservative forces) and the other group with the process-variant of the same approach (e.g., discussing system’s states and processes like in thermodynamics). For both variants, only three hours of system-based teaching proved to substantially improve the students’ level of LCME understanding compared to the level of understanding they had after conventional teaching. It follows that the system approach may work well at the upper-secondary level, if it is introduced through the scaffolding-and-fading technique. Keywords: quasi-experiment, mechanical energy, teaching materials, teaching strategies

Implementation of high-precision inertial reference for Taiji-1 satellite and its ground evaluation based on torsion pendulum system

As the key measurement load of Taiji-1 satellite, inertial sensor detects the acceleration disturbance of test mass (TM) under nonconservative force in line with the basic principle of capacitive sensing, while keeping the TM in equilibrium position through electrostatic drive. In order to ensure the smooth progress of the mission, it is necessary to test and evaluate the performance of inertial sensor on the ground. In this paper, a torsion pendulum system is designed to eliminate the influence of the Earth’s gravity so as to meet the requirements of ground test. The experimental results show that the inertial sensor in closed-loop control mode can stably keep the TM at equilibrium position. At the same time, the ground detection of acceleration resolution of inertial sensor is greatly affected by ground vibration noise. If the inertial sensor operates normally in space, its acceleration resolution can reach[Formula: see text], thus meeting the requirement of Taiji-1.

First result of orbit verification of Taiji-1 hall micro thruster

The Hall Micro Thrusters (HMTs) use cold gas or accelerated plasma dual mode to provide ultra-precise spacecraft altitude control. They were operated in space for the first time as part of the demonstration payloads on Chinese Academy of Science’s (CASs) Taiji-1 spacecraft since September 2019. Hall Micro Thruster Assemblies (HMTAs) were the actuators in drag-free control, and will compensate the nonconservative force for gravity wave observatories. The HMTAs meet the requirements of operating at 5–100 [Formula: see text] N of thrust with 0.7 [Formula: see text] N resolution and [Formula: see text]0.6 [Formula: see text] N/Hz[Formula: see text] (0.01–1 Hz) noise to deliver the nanometer-level precision control as fast as 30 ms measured by Gravitational Reference Sensor (GRS). A transfer function model in z-domain was fit and used to filter HMTs cathode voltage to predict GRSs thrust noise response. Simulations of a single or dual-frequency disturbance and the corresponding compensation demonstrated that HMTAs could deliver the required thrust profile expected. The capability to meet the requirements of thruster noise in drag-free control is critical for future missions because the acceleration noise on test mass directly relates to the gravity wave signa l. Preliminary in-orbit verification of Taiji-1 has showed HMTAs’ great potential in future, and the data in the experiments are presented in this paper.

Influence of Material-Dependent Damping on Brake Squeal in a Specific Disc Brake System

The connection of two phenomena, nonconservative friction forces and dissipation-induced instability, can lead to many interesting engineering problems. We study the general material-dependent damping influence on the dynamic instability of disc brake systems leading to brake squeal. The effect of general damping is demonstrated on minimal and complex models of a disc brake. Experimental analyses through the frequency response function (FRF) show different damping of the brake system coalescent modes, indicating possible dissipation-induced instability. A complex system including material-dependent damping is defined in commercial finite element (FE) software. A FE model validated by experimental data on the brake-disc test bench is used to compute the influence of a pad and disc damping variations on the system stability using complexe igenvalue analysis (CEVA). Numerical analyses show a significant sensitivity of the experimentally verified unstable mode of the system to the ratio of the damping between the disc and the friction material components.

Influence of the Low-Frequency Error of the Residual Orbit on Recovering Time-Variable Gravity Field from the Satellite-To-Satellite Tracking Mission

When using the dynamic approach to recover the time-variable gravity field, the reference orbit generated by the perturbation model and the non-conservative force observed from the accelerometer should be introduced at first, and then the observation equations of the residual orbit and the residual range rate are established. This introduces a perturbation model error and instrument noise. Thus, there are low-frequency errors in the residual orbit and the residual range rate. Currently, most studies only focus on the low-frequency error of the residual range rate, neglecting the influence of the low-frequency error in the residual orbit. Therefore, under the condition of the perturbation model error and instrument noise including the constant term and 1CPR term, the low-frequency error formulas of the residual orbit and residual range rate are derived according to the characteristics of the solution of the Hill equation. Then, the influence of the low-frequency error on the residuals is analyzed by using the simulation and the real data processing respectively. In the simulation and real data processing, the accuracy of the recovered gravity field can maintain a good consistency for different arc lengths by removing the low-frequency error in the residual orbit. Finally, the time-variable gravity field model UCAS-IGG (University of Chinese Academy of Sciences-Institute of Geodesy and Geophysics) was solved from January 2005 to February 2010 by removing the low-frequency error of the residual orbit and residual range rate. Compared with the official institutions, the UCAS-IGG presents a good consistency in the estimating time-variable gravity field signal. This study demonstrates how the effect of the low-frequency error of the residual orbit should be taken into consideration when the longer arc length is used to recover a time-variable gravity field. Using a long arc length can reduce the variables of the initial state and recover the influence of the small force.

Inclusion of Non-Conservative Forces in Geometric Integrators with Application to Orbit–Attitude Coupling

In this paper, a discretization method for incorporating nonconservative forces in a class of geometric numerical integrators known as variational integrators and Galerkin variational propagators is proposed. The proposed method does not require modification of the original integration algorithm used in conservative systems. First, the damped harmonic oscillator is used as benchmark for evaluating the proposed approach. Two more complex scenarios are presented next: one considering propagations in the two-body problem with drag forces, and another dealing with long-term translational propagations about small bodies considering orbit–attitude coupled force terms where the attitude is prescribed. Numerical experiments are performed, comparing results to a nominal analytical solution when it is available, or against a highly accurate propagated reference trajectory. The results in this paper show that including the nonconservative forces in the potential energy term for the discrete equations produces a very accurate discretization. This allows one to perform accurate and fast long-term numerical propagations with structure preserving variational algorithms, in scenarios where perturbations to the system can be modeled as nonconservative forces.

Relativistic mechanics and thermodynamics: II. A linear translation Hamiltonian–Lagrangian formalism

A relativistic Hamiltonian–Lagrangian formalism for a composite system submitted to conservative and non-conservative forces is developed. A block descending an incline with a frictional force, mechanical energy dissipation process, is described, obtaining an Euler–Lagrange equation including a Rayleigh’s dissipation function. A cannonball rising on an incline, process evolving with mechanical energy production, is described by an Euler–Lagrange equation including a Gibbs’ production function, with a chemical origin force. A matrix four-vector mechanical equation, considering processes’ mechanical and phenomenological aspects, is postulated. This relativistic Hamiltonian–Lagrangian four-vector formalism complements the Einstein–Minkowski–Lorentz four-vector fundamental equation formalism. By considering a process’ mechanical and thermodynamic description, temporal evolution equations, relating process’ Hamiltonian (mechanical energy) evolution and the involved thermodynamic potentials (entropy of the universe, Helmholtz free energy, Gibbs free enthalpy) variations, are obtained.

Research on Non-conservative Phenomena in Physics

Non-conservative phenomena are very common and very important in physics. They have the characteristic of work divergence (if an object moves under non-conservative force, the work it does is related to the path) and this phenomenon does not satisfy the time reversal invariance. Therefore, they can cause many situations. From a mathematical point of view, they are similar to divergence in infinite series. Therefore, the infinite series can analyze non-conservative phenomena. This paper takes non-conservative force as an example to prove the relationship between non-conservative force and infinite series.

Spatial distributions of nonconservatively interacting particles.

Certain types of active systems can be treated as an equilibrium system with excess nonconservative forces driving some of the microscopic degrees of freedom. We derive results for how many particles having both conservative and nonconservative forces will behave. Treating nonconservative forces perturbatively, we show how the probability distribution of the microscopic degrees of freedom is modified from the Boltzmann distribution. We then derive approximate forms of this distribution through analyzing the nature of our perturbations. We compare the perturbative expansion for the microscopic probability distribution to an exactly solvable active system. Finally, we consider how the approximate forms for the microscopic distributions we have derived lead to different macroscopic states when coarse grained for two different kinds of systems, a collection of motile particles, and a system where nonconservative forces are applied in space. In the former, we are able to show that nonconservative forces lead to an effective attractive interaction between motile particles, and in the latter we note that by introducing nonconservative interactions between particles we modify densities through extra terms which couple to surfaces. In this way, we are able to recast certain active problems as the statistical mechanics of nonconservative forces.